Adrian, at the time when Darcy tells Elizabeth that there is someone in the party "who more particularly wishes to know you", Georgiana does not know that Lizzy is at Pemberley (they are to arrive tne next day, and there was no mobile phone then to inform anyone on the road of what was expecting them :-)).

So Georgiana's wish to meet Elizabeth stems from an earlier time (maybe indeed she just mentioned it as a wishful thinking when hearing her praise by Fitzwilliam).